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Abstract
An extension of a finite volume scheme for three-dimensional Maxwell’s equations with discontinuous dielectric permittivity on tetrahedral meshes is discussed. The scheme is second order accurate in time and space for regions with linear and curvilinear discontinuities. It was tested on problems with linear and curvilinear discontinuity configurations. The test results support the second order accuracy of the proposed scheme.
Highlights
The time-dependent Maxwell’s equations describe the propagation and diffraction of the electromagnetic waves
The scheme is second order accurate in time and space for regions with linear and curvilinear discontinuities. It was tested on problems with linear and curvilinear discontinuity configurations
This leads to a reduced order of approximation for such cases. Another approach that does not have this shortcoming is the finite volume time domain method (FVTD). It relies on structured non-cartesian grids and unstructured meshes
Summary
The time-dependent Maxwell’s equations describe the propagation and diffraction of the electromagnetic waves. Another approach that does not have this shortcoming is the finite volume time domain method (FVTD) It relies on structured non-cartesian grids and unstructured meshes. As a result it can represent curvilinear boundaries more precisely and can preserve the second order of approximation for such cases. For FVTD the use of continuous variables for linear discontinuities in two dimensions was suggested in [4] and extended to three dimensions and curvilinear discontinuities in [5] This approach increased the accuracy but did not preserve the second order of approximation. In [6, 7] a simple approach to the gradient calculation and limitation was suggested that allowed to preserve second order of approximation for the Maxwell’s equations with discontinuous electromagnetic properties. For both cases the computational results support the second order of approximation
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